I’ve always been fascinated by the mathematics of gambling games. I was speaking at the Visual Studio Live Conference last week. VS Live is a conference for software developers who use the Microsoft technology stack. The event has been around for quite a number of years. VS Live has events in several cities; the one I was at was in Las Vegas.

I like conferences in Vegas, as opposed to other cities like San Francisco, because the hotel room rates are relatively inexpensive (my room was $109 per night), and there are tons of nice restaurants (although I’m more of a Taco Bell kind of person), and there are lots of interesting things to see.

I spotted two new gambling games I’d never seen before. As far as I can tell both games were introduced during the past year. The first game is called “High Card Flush” and was at the Planet Hollywood casino. It’s difficult to explain the game, but briefly, it’s a table game where each player antes $10 and then all players and the dealer get seven cards face down. Players play against the dealer, not each other. After the deal, each player puts together the most cards of the same suit, maybe for example, a King of clubs, a Ten of clubs, and a Seven of clubs, from the seven-card hand. Then if the player has three or more of the same suit, the player has the option to increase their bet. After betting, the dealer makes her best flush hand. If the player’s hand is better he wins. I’m leaving out a lot of details.

So, in essence the only real decision to make is whether to add an additional bet after the ante or not. Normally, I don’t like games where there are few or no decisions to be made (games like craps and roulette for example). But High Card Flush was kind of fun. There’s sort of an artificial sense that you’re making a decision by pulling your best flush hand from your seven cards. But there’s really not much happening — your best hand is almost immediately obvious. Anyway, the single High Card Flush table at Planet Hollywood was always packed every time I walked by it. I have no idea what the house edge might be, or, more importantly, if a player could gain an advantage by knowing other player’s cards.

The second new game I saw was across the street at the Aria casino. The game is called “Free Bet Blackjack”. It’s like normal Blackjack except if a player has a 9, 10, or 11 total on his first two cards, instead of doubling down like usual, amazingly, the house will place the bet for you for free. Furthermore, the house will also place a free bet for you if you split a pair. The catch is that the dealer pushes if she gets a 22 total. My first reaction was that this is impossible — it seems like a huge advantage for the player, but of course, the house still has an edge.

I enjoyed thinking about the math behind Free Bet Blackjack. I played for a while and was slowly losing until this hand: I had bet $15 and got a pair of 9s, dealer had a 5 showing. Perfect. I split the 9s and the dealer placed the free $15 for the second 9 hand for me (it’s actually a gold-colored marker). On my first 9 I got an Ace for a total of 20. Nice! On my second 9 I go another 9. Nicer! I split those and the dealer placed another free $15 bet. On one of the new 9s I got another 9. And on one of the new hands I got yet another 9. (The game is dealt from a shoe with, I think, eight decks). Anyway, the entire table was pretty excited, and even better, the three other guys at the table were all expert players so they could appreciate how rare this situation with five hands was. The dealer busted and I won 5 * $15 = $75 for a single $15 bet. Nice!

Let me emphasize that I don’t enjoy gambling for its own sake. There’s something that’s just not entirely right about gambling in a casino environment. I do enjoy placing a friendly bet on the outcome of a sports game, but only because it makes watching the game more interesting. But I do like to analyze casino games as entertaining problems in applied mathematics.